<h2>Problem 263</h2>
<div style="color:#666;font-size:80%;">07 November 2009</div><br />
<div class="problem_content">
<P>
Consider the number 6. The divisors of 6 are: 1,2,3 and 6.<BR />
Every number from 1 up to and including 6 can be written as a sum of distinct divisors of 6:<BR />
1=1, 2=2, 3=1+2, 4=1+3, 5=2+3, 6=6.<BR />
A number <var>n</var> is called a practical number if every number from 1 up to and including <var>n</var> can be expressed as a sum of distinct divisors of <var>n</var>.
</P>
<P>
A pair of consecutive prime numbers with a difference of six is called a sexy pair (since "sex" is the Latin word for "six"). The first sexy pair is (23, 29).
</P>
<P>
We may occasionally find a triple-pair, which means three consecutive sexy prime pairs, such that the second member of each pair is the first member of the next pair.
</P>
<P>
We shall call a number <var>n</var> such that :
<UL>
<LI>(<var>n</var>-9, <var>n</var>-3), (<var>n</var>-3,<var>n</var>+3), (<var>n</var>+3, <var>n</var>+9) form a triple-pair, and 
<LI>the numbers <var>n</var>-8, <var>n</var>-4, <var>n</var>, <var>n</var>+4 and <var>n</var>+8 are all practical,
</UL> 
an engineers&rsquo; paradise.
</P>
<P>
Find the sum of the first four engineers&rsquo; paradises.
</P>


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